On simultaneous Chebyshev approximation in the “sum” norm
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- by William H. Ling PDF
- Proc. Amer. Math. Soc. 48 (1975), 185-188 Request permission
Abstract:
Let ${f_1},{f_2}$ be real valued functions on $[a,b]$ and let $S$ be a nonempty family of real valued functions on $[a,b]$. It is shown that the simultaneous approximation of ${f_1}$ and ${f_2}$ in the “sum” norm by elements of $S$ is, with one restriction, equivalent to the approximation of the arithmetic mean, $({f_1} + {f_2})/2$. A complete characterization of best approximations in the “sum” norm is given including results for varisolvent families.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 48 (1975), 185-188
- MSC: Primary 41A30; Secondary 41A50
- DOI: https://doi.org/10.1090/S0002-9939-1975-0361555-4
- MathSciNet review: 0361555